A note on the asymptotics for the randomly stopped weighted sums

作者：Yang, Yang^*; Shi, Xi-Xi; Huang, Xing-Fang

来源：Nonlinear Analysis: Modelling and Control , 2018, 23(2): 204-212.

DOI：10.15388/NA.2018.2.4

• asymptotics
• randomly weighted sums
• heavy tail
• widely orthant dependence

Let {X-i, i >= 1} be a sequence of identically distributed real-valued random variables with common distribution F X; let {theta(i), i >= 1} be a sequence of identically distributed, nonnegative and nondegenerate at zero random variables; and let tau be a positive integer-valued counting random variable. Assume that {X-i, i >= 1}, {theta(i), i >= 1} and tau are mutually independent. In the presence of heavy-tailed X-i ' s, this paper investigates the asymptotic tail behavior for the maximum of randomly weighted sums M-tau = max(1 <= k <=tau) Sigma(k)(i=1) theta X-i(i) under the condition that {theta(i), i >= 1} satisfy a general dependence structure.

• 出版日期2018
• 单位南京审计大学